"While using the Mantis Cruiser, kill the last enemy with your last crew member on their ship."
To earn the achievement, there must be only one crewmember currently employed onboard the player's ship. The sole crewmember needs to teleport to the enemy ship and kill the last enemy crew (deal the final hit).
This achievement can be unlocked with the assistance of a Boarding Drone, but the final hit must be dealt by the crewmember.
Clone Bay allows to get this achievement without losing or getting rid of any crew. The game regards crew in the cloning queue as dead. The Backup DNA Bank augmentation makes attaining this achievement more trivial.
The achievement can also be earned if one of the two available crewmembers (e.g. the Mantis B starting crew) gets mind-controlled at the time of the final hit to the enemy crew.
This achievement cannot be obtained by killing the Rebel Flagship's crew, likely because the final kill must trigger a victory, and the Flagship has an AI that takes over.